© William James Calhoun, 2001 4-1: Ratios and Proportions OBJECTIVE: You need to be able to solve proportions using cross-multiplication. Initial terms:

© William James Calhoun, 2001

4-1: Ratios and Proportions

OBJECTIVE:You need to be able to solve proportions using cross-multiplication.

Initial terms:•ratio - a comparison of two numbers by division•proportion - an equation stating that two ratios are equal

Ratios can be written in different ways. Examples:

x to y x:y

Proportions will look like a fraction equal to a fraction. If there are no variables in the proportion, then both fractions should reduce to the same fraction for the proportion to be true.

Example:

15

30

5

10 This is the proportion.

Both fractions reduce to2

1

2

yx



In a proportion, the product of the extremes is equal to the product of the means.

If then ad = bc.

4.1.1 MEANS-EXTREMES PROPERTY OF PROPORTIONS

db

ca

Why someone named them is beyond me and you will not be required to remember this.

What you really need to remember is: cross-multiply to solve fraction = fraction.

db

ca

ad bc=


EXAMPLE 1: Use cross products to determine whether each pair of ratios forms a proportion.

A. B.18

12,

3

2

2.5

4.3,

6

5.2


If these two fractions form a proportion, then they must be equal to each other, so:

23

1218

=?

Now, cross multiply to see if the proportion is true.

2(18) 3(12)=?

36 36=

This pair of numbers is a proportion.

If these two fractions form a proportion, then they must be equal to each other, so:

2.56

3.45.2

=?

Now, cross multiply to see if the proportion is true.

2.5(5.2) 6(3.4)=?

13 20.4

This pair of numbers is NOT a proportion.



•scale - a ratio used to make models to represent things that are too large or too small to be conveniently drawn at actual size

The scale compares the size of the model to the actual size of the object being modeled.

Another term:

The next example is really BIG

With sharp teeth….

No, it is not a vorpal bunnie.


EXAMPLE 2: In a recent movie about dinosaurs, the dinosaurs were scale models and so was the sport utility vehicle that the T-Res overturned. The vehicle was made to the scale of 1 inch to 8 inches. The actual vehicle was about 14 feet long. What was the length of the model sport utility vehicle?Some of the measurements in the problem are in inches, and some are in feet. To make the problem easier - and so we do not need to keep up with units, we will get all the numbers in the same units. It is easiest to turn the 14 feet into inches.

14 ft = 168 in

168

m

8

1

scale

actual

cross multiply

1(168) = 8m 168 = 8m

solve this equation

168 = 8m

m = 21The length of the vehicle was 21 inches long. (13/4ft.)


88


EXAMPLE 3: Solve each proportion.

A. B.

5(m) = 4.25(11.32)5m = 48.115 5m = 9.622

15x = 3(x + 5)Cross multiply.

Distribute.

Move the x’s on the right by…

subtracting 3x from both sides.

15x = 3x + 15-3x -3x

12x = 15

Divide by 12 on both sides.

12 12

x = 1.25


m32.11

25.45

155x

3x

Cross multiply.

And another term:•rate - ratio of two measurements having different units of measure

For example, 30 miles per gallon is a rate.Proportions are often used to solve problems involving rates.


HOMEWORK

Page 199#15 - 33 odd


Documents

© William James Calhoun, 2001 4-1: Ratios and Proportions OBJECTIVE: You need to be able to solve proportions using cross-multiplication. Initial terms: